Random forest with acceptance–rejection trees

  • Peter Calhoun
  • Melodie J. Hallett
  • Xiaogang Su
  • Guy Cafri
  • Richard A. Levine
  • Juanjuan FanEmail author
Original Paper


In this paper, we propose a new random forest method based on completely randomized splitting rules with an acceptance–rejection criterion for quality control. We show how the proposed acceptance–rejection (AR) algorithm can outperform the standard random forest algorithm (RF) and some of its variants including extremely randomized (ER) trees and smooth sigmoid surrogate (SSS) trees. Twenty datasets were analyzed to compare prediction performance and a simulated dataset was used to assess variable selection bias. In terms of prediction accuracy for classification problems, the proposed AR algorithm performed the best, with ER being the second best. For regression problems, RF and SSS performed the best, followed by AR, and then ER at the last. However, each algorithm was most accurate for at least one study. We investigate scenarios where the AR algorithm can yield better predictive performance. In terms of variable importance, both RF and SSS demonstrated selection bias in favor of variables with many possible splits, while both ER and AR largely removed this bias.


Classification and regression trees Supervised learning Prediction Variable selection bias Ensemble methods 



This research was supported in part by NSF Grant 163310.

Supplementary material

180_2019_929_MOESM1_ESM.pdf (123 kb)
Supplementary material 1 (pdf 123 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Peter Calhoun
    • 1
  • Melodie J. Hallett
    • 2
  • Xiaogang Su
    • 3
  • Guy Cafri
    • 4
  • Richard A. Levine
    • 5
    • 6
  • Juanjuan Fan
    • 6
    Email author
  1. 1.Jaeb Center for Health ResearchTampaUSA
  2. 2.Department of SociologySan Diego State UniversitySan DiegoUSA
  3. 3.Department of Mathematical SciencesUniversity of TexasEl PasoUSA
  4. 4.Johnson & Johnson Medical DevicesSan DiegoUSA
  5. 5.Analytic Studies and Institutional ResearchSan Diego State UniversitySan DiegoUSA
  6. 6.Department of Mathematics and StatisticsSan Diego State UniversitySan DiegoUSA

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